Unwanted lines showing up on rendered cube
Every quad is treated as 2 triangles, this is what is causing the problem. You need smooth shading for the edges inside the quads and sharp for the corners of the cube.

To do this set the smoothing to smooth and in the mesh properties check the auto-smooth option and set the angle for cca. 70° (depends on the twisting).





This way faces with angle with more than 70° will keep sharp shading between them.

You should also densify the geometry so it follows the ideal curved/bended surface closer.